Exponentially weighted supremum norm
= Exponentially weighted supremum norm
{title2=$\|u\|_\alpha=\sup_te^{-\alpha t}\|u(t)\|$}
On continuous functions $u:[0,T]\to X$, the exponentially weighted supremum norm is $\|u\|_\alpha=\sup_{0\leq t\leq T}e^{-\alpha t}\|u(t)\|$. It is equivalent to the ordinary supremum norm and often turns a Volterra integral map into a <contraction mapping>.